exploring a pseudo-regression model of transnational cooperation in science

Jointly published by Akadémiai Kiadó, Budapest Scientometrics,

and Kluwer Academic Publishers, Dordrecht Vol. 56, No. 3 (2003) 403–416

Received November 11, 2002.

Address for correspondence:P. S. NAGPAUL

205 D Green Apartments (MIG), Rajouri Garden, New Delhi 110027, IndiaE-mail: [email protected]

0138–9130/2003/US $ 20.00Copyright © 2003 Akadémiai Kiadó, BudapestAll rights reserved

Exploring a pseudo-regression model oftransnational cooperation in science

P. S. NAGPAUL

New Delhi (India)

This paper reports the results of an empirical study on the impact of three proximity measures:geographical distance, thematic distance and socio-economic distance among the set of 45scientifically most advanced countries on their cooperation network.

In network data, individuals (viz. countries) are linked to one another and the relationships arenested and embedded in groups, with the result that statistical assumptions of independenceunderlying ordinary least squares regression are systematically violated. Hence, we have used anon-parametric regression procedure, Quadratic Assignment Procedure (QAP), for regressing thematrix of transnational cooperation on the matrices of three proximity measures: geographicproximity, thematic proximity and socio-economic proximity. The results indicate that all thethree proximity measures have the expected negative effect on transnational cooperation.Geographic proximity has greater impact than the other proximity measures.

Introduction

Transnational cooperation is becoming ever more frequent and is playing a moreimportant role in the production of scientific knowledge. It is estimated that in thedecade between 1982-1984 and 1992-1994, publication output of 45 scientifically mostadvanced countries increased by 2.6% per annum, whereas the number of transnationalcooperation links increased by 11.1% per annum. Moreover, duringthis period, the number of empty cells of the collaboration matrix of these countries(45 u 45-adjacency matrix) decreased from 18% to 4% (Nagpaul, 1997). These resultsimply that transnational cooperation has become not only more intensive but also moreextensive. According to Schott (1998), long-distance links have grown even faster thanlinks to neighboring countries, thus indicating an increase in the global span ofscientific collaboration. Significantly, this has happened despite socio-cultural,linguistic and political barriers. However, different regions of the world have notexperienced the same level of growth in transnational cooperation (Nagpaul, 1999).

Multi-country publications are found to receive more citations than single countrypublications (Narin & Whitlow, 1990). Hence, it can be assumed that multi-country

P. S. NAGPAUL: Transnational cooperation in science

404 Scientometrics 56 (2003)

publications constitute a more important segment of the world literature. Theirimportance can be gauged by the fact that bibliometric data on multi-countrypublications have received widespread attention of science policy institutions andresearch scholars. According to Dobrov (1979), the importance of internationalcooperation is growing rapidly for all countries, without exception, and in some respectsfor the fate of the world as a whole. Ziman (1994) argues that the increased cost ofcertain instruments, the increased scope of many problems, the global reach of research-intensive multinational companies, and increased travel and communication arecombining to make the scientific community even more transnational – research havingalways been a more international pursuit than most other professions.

However, all the countries do not have the same level of access to the transnationalnetwork, nor do they have the same pattern of access in the choice of partner countriesor research fields for cooperation (Nagpaul & Sharma, 1994). Obviously, thesedifferences originate from a variety of contextual factors, which affect theirparticipation in the transnational network. The literature on the subject is extensive(Beaver & Rosen, 1979), but by and large speculative; it suggests a long list of factors,which can be classified into two broad categories: socio-cognitive and geo-political.Scientific cooperation is essentially a social process and there are probably as manyreasons for researchers to collaborate as there are reasons for people to communicate.

Several studies are reported in the literature on the effects of spatial and socialdistance on oral (i.e., face-to-face) communication between individual scientists (see forexample: Pruthi & Nagpaul, 1978). Spatial distance implies physical hurdles in makinga contact, such as geographic distance, climbing stairs, etc. Social distance impliespsychological hurdles in making a contact, such as differences in rank, academic status,conflict of interests, etc. These studies indicate that the frequency of communicationbetween two individuals is inversely proportional to the square of the distance.According to Allen & Fusfeld (1975), ‘probability of communication reaches a lowasymptotic level within the first 25-30 metres’. Moreover, equi-status scientistscommunicate more frequently than scientists of unequal status (Pruthi & Nagpaul,1978). However, there are hardly any empirical studies on the effects of such contextualfactors on scientific collaboration; notable exceptions being the studies by Katz (1994)and Cabo (1994).

Katz (1994) examined the effect of geographic distance on the frequency of intra-country collaboration between universities in three countries – U.K., Canada andAustralia. He fitted the regression equation, y=ae–bd , where y is the frequency ofbilateral cooperation and d is the geographic distance. He found that the parameter bwas negative, but its value differed between countries.


Scientometrics 56 (2003) 405

Cabo (1994) examined the effect of cultural differences on the participation ofresearch organizations from different countries in international projects. He found thatcultural differences had the expected effect (i.e., negative sign) but the values were lowand only a few were statistically significant.

In this paper we examine empirically the following research questions:

1. What is the impact of geographic proximity on international cooperation? Dothe countries that are geographically proximate have relatively morecooperation than those located far apart?

2. Do the countries that have similar levels of socio-economic developmentcooperate more than those who have dissimilar levels of socio-economicdevelopment?

3. Do the countries that have similar profiles of research cooperate more thanthose who have dissimilar profiles of research? To quote Kretschmer (1999), dothe birds of the same feather flock together or unlike poles attract each other?

Methodology

Measurement of cooperation

Transnational cooperation is defined in terms of articles cosigned by authors fromtwo or more countries. An important, but controversial, issue in coauthorship analysis ishow to assign the credit of a coauthored article to the partner countries. Suppose anarticle is authored by five researchers, two in India, one in Japan, one in China and onein USA. It can be easily seen that there are six bilateral links: [India, USA] [India, China] [India, Japan] [Japan, USA] [China, USA] [China, Japan].

Since, the primary concern of this study is not internationally coauthotrd articles butinternational linkages they involve, we have adopted the ‘whole count’ method inpreference to ‘fractional counting’. In the whole count method, a link between any twocountries would be counted as 1, whereas in the fractional counting method, it would becounted as 1/6. Here, we assume that a link between any two countries is always a fixedsingle unit, which does not vary with the number of countries involved in a coauthoredarticle.



The data

Transnational cooperation

The data on co-authorship links of 45 scientifically most advanced countries werecollected by dyadic search from the CD-ROM version of Science Citation Index (SCI)for three indexing years: 1992-1994. The names of the countries are given in theAppendix. The data on co-authorship links was tabulated in the form of an adjacencymatrix

C = ~cij~,

where cij denotes the number of cooperation links between country i and country j.Obviously, cii = 0. Since the links are bidirectional, the matrix is symmetric.

Geographic proximity

There are two alternative approaches for constructing the matrix of inter-countrydistances:

1. Use an accurate scale map of the world and measure the distance between thecapitals of various countries by a foot ruler.

2. Use the distance calculated by the Airlines companies for pricing the air tickets.

We have opted for the second alternative, which is assumed to be more realistic. Thematrix of geographic proximities (D) is defined as follows:

D = ~dij~,

where dij is the distance between the capital cities of countries i and j. Obviously,dii = 0, since the distance between a country with itself is zero.

Thematic proximity

Thematic proximity between a pair of countries is defined by the similarity of theirresearch profiles. The matrix of thematic proximities was constructed as follows:

Firstly, the data on publication output of these countries during 1989-1993 weretaken from Braun et al. (1995). The publications are classified into 27 fields:



Mathematics, Materials Science, Electronics Engineering, Nuclear Sciences,Mechanical & Civil Engineering, Inorganic Chemistry & Engineering, AnalyticalChemistry, Physical Chemistry, Organic Chemistry, Applied Physics, Solid- statePhysics, Geosciences, Other Physics, Ecology, Food Science & Agriculture,Biotechnology, Microbiology, General Biology, Pharmacology & Pharmacy, PublicHealth, Pathology, Neurosciences, Reproduction Medicine & Geriatrics, GeneralMedicine, Internal Medicine, Research Medicine, Immunology.

The data were tabulated in the form of a rectangular matrix:

A = ~aij~,

where aij denotes the number of articles of country i in field j.This matrix was transformed into a matrix of thematic proximities, T, by computing

the Pearson correlation between the pairs of countries.

T = ~rij~;

T is a square matrix, whose elements. rij represent Pearson correlation betweencountries i and j.

Socio-economic proximity

Socio-economic proximity between a pair of countries was measured by theproximities of their socioeconomic profiles, defined by the following four indicators: (i)Human Development Index, (ii) GNP per capita, (iii) Economic Structure, and (iv)Adult Literacy Rate.

Human development index (HDI) has three components: life expectancy at birth,educational attainment, and comprising adult literacy with two thirds weight and acombined primary, secondary and tertiary enrolment ratio, with one third weight; andincome. The HDI value for each country indicates how far that country has to go toattain certain defined goals: an average life span of 85 years, access to education for alland a decent level of income.

GNP per capita was measured on purchasing power parity (PPP) scale, instead ofexchange rate. The PPP-conversion factor is defined as the number of units of acountry’s currency required to buy the same amounts of goods and services as onedollar should buy in USA. The economic structure was operationalized by thecontributions of three economic sectors, viz. Agriculture, Industry and Services inpercentage terms to the GNP. Adult Literacy Rate means the percentage of adults in acountry who are literate.



The matrix of socio-economic proximities was constructed as follows.Firstly, the data on socio-economic indicators (except Human Development Index)

were taken from the World Development Report (World Bank, 1995). The data onHuman Development Index were downloaded from the website of The Economist. Thedata were tabulated in the form of a rectangular matrix

E = ~eij~,

where eij indicates the value of indicator j for country i. This matrix was transformedinto a matrix of socioeconomic proximities, S, by computing the Euclidean distancebetween pairs of countries i, j.

Analysis and results

The effects of geographic, thematic and socioeconomic proximities on transnationalcooperation were analyzed by setting up the following pseudo-regression model.

C= a0 + a1 u D + a2 u T + a3 u S + Hwhere C is a matrix of transnational cooperation, and D, T and S are respectively thematrices of geographic, thematic and socio-economic proximities and H denotes theerror terms. Error terms are assumed exogenous with mean zero, but need not behomoscedastic, nor independently distributed. Since, as argued below, this modelviolates the fundamental assumptions of ordinary least squares (OLS) regression; wehave called this model a pseudo-regression model.

In network data, individuals are linked to one another and relations are nested andembedded in groups. Hence, network data can not be assumed to consist of independentobservations, but rather have varying amounts of dependencies according to which rowor column they belong to. Dyadic and higher order interdependencies may exit in thedata with the result that the statistical assumptions of independence on which OLS isbased are systematically violated. Hence, we have used an alternative method –Quadratic Assignment Procedure (QAP) – for estimating the effects of differentproximity measures on the structure of international cooperation.

Quadratic Assignment Procedure was first suggested for the bivariate case byHubert and others (Hubert & Shultz, 1976; Backer & Hubert, 1981: Hubert & Colledge,1981), and extended to the case of multiple regression by Krackhardt (1988). Thisapproach is found to be robust against a wide array of sources of autocorrelation.



QAP regression

This procedure involves the following steps:

1. Vectorize the dependent matrix. Take each element of the 45 u 45 adjacencymatrix C and construct a column vector by successively placing below thevector of the first element the vectors of subsequent elements. Each columnvector consists of 44 elements (since the element corresponding to the diagonalof the matrix is empty). As there are 45 rows, the resultant vector would havelength equal to 45 u 44.

2. Vectorize each regressor matrix in the same way as for C.3. Regress the dependent variable on the explanatory variables using ordinary

least squares, and obtain point estimates of regression coefficients and multiple R2.

The resulting coefficients are unbiased, even if the data are autocorrelated (Judgeet al., 1990; p. 27). The problem, however, is that traditional estimates of standarderrors of these coefficients are very sensitive to autocorrelation in the data. Hence theyperform poorly for statistical significance tests.

QAP regression avoids this problem by generating a null hypothesis referencedistribution against which the observed coefficients are compared. This referencedistribution is created as follows:

x Randomly permute the rows and columns of the dependent matrix C, but notthose of the regressor matrices. Re-compute the OLS regression as in Steps 1-3and store the resulting coefficients. Repeat this large number of times.

x Estimate the standard error of the regression coefficients from the distributionof estimates obtained in the above step or alternatively count the number ofrandom permutations that yielded a coefficient as extreme as the one computedin Step 3. This proportion can be treated as the ‘level of statistical significance’.In this paper, we have adopted the latter procedure.

A significant feature of QAP is the nature of permutation of the dependent matrix,which is of a restricted form: All rows and columns of the matrix are permutedidentically. For example, if row 5 and row 8 are switched, then columns 5 and 8 are alsoswitched. This form of permutation is essentially a ‘relabeling’ of the matrix (i.e., thecountries switch places), with the result that the structure of the matrix remainsunchanged under each permutation. It is the nature of this permutation that permitsthe test to be quite robust against the kind of autocorrelation encountered in thenetwork data.



Normalization of matrices

The dependent and independent matrices were normalized (to remove theconfounding effects of size) before submitting them to the QAP–regression algorithm.

The matrix of transnational cooperation, C, is confounded by the size of thecountries involved. Since we are basically interested in exploring the effects of differentproximity measures on the structure of cooperation links, the confounding effect of sizehad to be removed. The matrix was normalized as follows: The rows and columns of thematrix were alternately divided by row or column sums, and the procedure was iterateduntil a symmetric matrix was obtained, whose total sum was 100.

The geographic proximity matrix, D, was normalized by multiplying each cell of thematrix by the reciprocal of the maximum geographic distance. The normalized matrixhad values in the range (H, 1), where H is a very small value.

The socio-economic proximity matrix, S, was also normalized by multiplying eachmatrix cell (Euclidean distance) by the reciprocal of the maximum value of theEuclidean distance in the matrix.

The thematic proximity matrix, T, had cell values in the range (–1, +1). This matrixwas normalized by a linear transformation of each cell:

dij = 2

)1( ijr�.

The normalized matrix had cell values in the range (0, 1). With this transformation,a high positive correlation receives a dissimilarity measure close to zero, whereas a highnegative correlation receives a dissimilarity measure close to 1.

Regression analysis

Two sets of regression analysis were carried out, one for each independentproximity matrix and the other for all the three independent proximity matricestogether. In each case, 999 random trials were made. Social network analysis softwareUCINET V (Borgatti et al., 1999) was used for this purpose.

Simple regression analysis

Table 1 presents the results of QAP- regression of transnational cooperation on eachof the three proximity matrices. The table gives the values of unstandardized regression



coefficient for each independent matrix, including the intercept, along with theproportion of random trials, yielding a coefficient as large or as small as the observedvalue. When the coefficient is positive, we consider the proportion as large and whenthe coefficient is negative we consider the proportion as small to test the statisticalsignificance of the coefficient The table also gives the value of R2, along with theproportion of random trials yielding an R2 as large as or larger than the observed value.

Table 1. Unstandardized coefficients from the regressions of transnational cooperation on(i) geographic distance, (ii) thematic distance and (iii) socio-economic distance

Geographical Distance

Variable Coefficient Proportion as Significance levelLarge Small (probability)

Intercept 3.344 0.000 1.000 0.000Geographic distance �4.519 1.000 0.000 0.000

Multiple R2 0.093 p = 0.000

Thematic Distance


Intercept 3.459. 0.000 1.000 0.000Thematic distance �3.580 1.000 0.000 0.000

Multiple R2 0.048 p = 0.000

Socio-economic Distance


Intercept 2.611 0.000 1.000 0.000Socio-economicdistance �1.028 1.000 0.000 0.000

Multiple R2 0.006 p = 0.006

Note: When the coefficient is positive, we consider the proportion as large and when the coefficient isnegative we consider the proportion as small for testing its statistical significance.. For example, in the case ofgeographical distance, none of the random trials yielded intercept as large as the observed value (3.344).Hence significance level = 0.000. Also, none of the random trials yielded regression coefficient as small as theobserved value (�4.519). Hence, significance level =0.000.



Geographic proximity

The value of R2 (0.093) is statistically highly significant (p � 0.001), since none ofthe random trials yielded an R2 as large as the observed value. The unstandardizedregression coefficient (�4.519) is also statistically highly significant (p � 0.001), sincenone of the randomly permuted dependent matrices produced a coefficient less than orequal to the observed value.

Thematic proximity

The value of R2 (0.048) is lower than that for geographical proximity, but stillstatististically highly significant (p � 0.001), since none of the randomly permuteddependent matrices yielded a value as large as the observed value. The value ofunstandardized regression coefficient (�3.580) is also statistically highly significant(p � 0.001), since none of the randomly permuted dependent matrices produced acoefficient less than or equal to the observed value.

Socio-economic proximity

The value of R2 (0.006) is quite low, but still statistically highly significant(p � 0.006), since only 0.6 percent of the randomly permuted dependent matricesyielded a value as large as the observed value. The value of unstandardized regressioncoefficient (�1.028) is also statistically highly significant (p � 0.001).

Multiple regression analysis

Table 2 presents the results of multiple regression analysis of transnationalcooperation on all the three proximity matrices together.

The value of R2 (0.120) is statistically highly significant (p � 0.001) since none ofthe random trials yielded an R2 as large as the observed value. The unstandardizedregression coefficients for geographic proximity (�4.058) and thematic proximity(�2.664) are statistically highly significant (p � 0.001). The unstandardized regressioncoefficient for socioeconomic proximity is statistically not significant (p � 0.23); morethan 23 percent of random permutations of the dependent matrix produced coefficientless than or equal to the observed value.



Table 2. Unstandardized regression coefficients from the regression of transnational cooperationon geographic, thematic and socio-economic proximities


Intercept 4.172 0.000 1.000 0.000Geographic distance �4.058 1.000 0.000 0.000Thematic distance �2.664 1.000 0.000 0.000Socio-economic distance �0.167 0.767 0.233 0.233

Multiple R2 0.120 p = 0.000

It may be recalled that in the simple regression analysis, socioeconomic proximityhad a significant negative effect on transnational cooperation, but in the presence ofother predictors, socio-economic proximity did not have statistically significant effect.Probably, this is due to the clustering of affluence and poverty in different geographicregions. Out of 25 high-income countries in our data, 15 countries are located inEurope; four in Asia where Japan, Singapore, Hong Kong and Taiwan are located closeto each other. Four upper middle-income countries in South America (Argentina, Chile,Mexico and Brazil) are located relatively close to each other. Two high-incomecountries, USA and Canada are located close to each other. The same is also true forAustralia and New Zealand.

Discussion

In this paper we have analyzed the effects of three proximity measures – geographicdistance, thematic distance and socio-economic distance – on the network oftransnational cooperation of 45 scientifically most advanced countries. This analysis isbased on the regression of the matrix of transnational cooperation on the threeproximity measures, using a bootstrapped Quadratic Assignment Procedure (QAP). Allthe three proximity measures are negatively related to transnational cooperation, but theunstandardized regression coefficient for socio-economic proximity does not reach thelevel of statistical significance.

The values of regression coefficients indicate that geographic distance is a moreimportant predictor of transnational cooperation than thematic distance, but its effectseems to have decreased over time (Schott, 1998; Nagpaul, 1999). This effect is likelyto decrease still further due to faster and cheaper modes of travel, increasing role of



international and regional agencies in the promotion and development of science, andnew communication technology which can enable scientists to collaborate at a distance.

It appears that countries cooperate with each other to gain or share their strengths indifferent fields. In a recent study (Nagpaul, 1998), it was observed that some of thestates of the Indian union were cooperating in the fields of their relative strength whilesome others were cooperating in their fields of relative weakness. This might as well betrue in the case of transnational cooperation. It appears that birds of the same feather aswell as of different feather are flocking together in the transnational network. If it is so,the relationship between thematic proximity and international cooperation is not likelyto be strong.

A major limitation of the study is that the data on transnational cooperation aredated, but this limitation is not very serious since our primary interest is on the structureand not the quantum of transnational cooperation. The structure is invariant; thedirection of relationships of contextual factors would remain the same, but themagnitude of relationships can change due to socio-economic, political andtechnological factors. None-the-less, the results of this study could be seen as abenchmark to assess the role of these contextual factors on transnational cooperation inthe future.

The values of multiple R2 and regression coefficients, issued by the QAP algorithm,indicate that the relationships are not strong, even though statistically highly significant.However, we do not expect massively strong relationships; one should be highlysuspicious if there were any. After all, transnational cooperation is a complex socio-political phenomenon and there are many factors that could influence the cooperationnetwork. In this study we have considered only three of them. Moreover, increasingglobalization of science seems to attenuate the effects of proximity measures consideredin this paper.

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Appendix

Argentina

Australia

Austria

Belgium

Brazil

Bulgaria

Canada

Chile

China

Czechoslovakia

Denmark

Egypt

Finland

France

Germany

Greece

Hongkong

Hungary

India

Ireland

Israel

Italy

Japan

Korea (South)

Mexico

Netherlands

New Zealand

Nigeria

Norway

Poland

Portugal

Romania

Russia

Saudi Arabia

Singapore

South Africa

Spain

Sweden

Switzerland

Taiwan

Turkey

United Kingdom

USA

Venezuela

Yugoslavia

exploring a pseudo-regression model of transnational cooperation in science

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